Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Extreme Precipitation Projections in a Changing Climate(2019) Hu, Huiling; Ayyub, Bilal M.; Civil Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Global climate is changing at an alarming rate, with an increase in heat waves, wildfires, extreme weather events, and rising sea levels, which could cost the United States billions of dollars in lost labor, reduced crop yields, flooding, health problems, and crumbling infrastructure. Reports by hundreds of US climate scientists from 13 federal agencies in the Fourth National Climate Assessment (2018) predict that the US economy will shrink by as much as 10% by the end of the century if global warming continues with current trends. Extreme precipitation, in particular, has led to significant damage through flooding, bridge scouring, land-slides, etc.; therefore, it is critical to develop accurate and reliable methods for future extreme precipitation projection. This dissertation proposes new methods of improved projections of such extremes by appropriately accounting for a changing climate. First, this dissertation studies how to model extreme precipitation using Markov Chains and dynamic optimization. By incorporating day-to-day serial dependency and dynamic optimization, the model improves the accuracy of extreme precipitation analysis significantly. The dissertation also examines future projections of extreme precipitation. State-of-the-art methods for future precipitation projections are based on downscaled Global Climate Models (GCMs), which are not always accurate for extreme precipitation projection. This work studies accuracy when using downscaled GCMs for extreme precipitation and designed new methods based on copulas to improve the accuracy. Finally, the above methods are applied to the analysis of future trends of intensity-duration-frequency (IDF) curves, which, in turn, have extensive applications in designing drainage systems. To incorporate geographic influence on local areas, a machine-learning-based solution is proposed and validated. The results show that the gradient boosting tree can be used to accurately project future IDF curves for short durations. It is also projected that short-duration intensity will increase up to 23% for the selected representative stations in this century. In summary, this dissertation systemically studies different aspects of improvements and applications of extreme precipitation projection. By using mathematical models, such as copula and Markov Chains as well as various machine-learning models (i.e., gradient boosting tree), extreme precipitation projection can be made significantly more reliable for use.Item Dependence Structure for Levy Processes and Its Application in Finance(2008-06-06) chen, qiwen; Madan, Dilip B; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this paper, we introduce DSPMD, discretely sampled process with pre-specified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified marginals and pre-specified dependence. In the DSPMD for Levy processes, some regular copula can be extracted from the discrete samples of a joint process so as to correlate discrete samples on the pre-specified marginal processes. We prove that if the pre-specified marginals and pre-specified joint processes are some Levy processes, the DSPMD converges to some Levy process. Compared with Levy copula, proposed by Tankov, DSPMD offers easy access to statistical properties of the dependence structure through the copula on the random variable level, which is difficult in Levy copula. It also comes with a simulation algorithm that overcomes the first component bias effect of the series representation algorithm proposed by Tankov. As an application and example of DSPMD for Levy process, we examined the statistical explanatory power of VG copula implied by the multidimensional VG processes. Several baskets of equities and indices are considered. Some basket options are priced using risk neutral marginals and statistical dependence. SRLMD is based on Rosinski's series representation and Sklar's Theorem for Levy copula. Starting with a series representation of a multi-dimensional Levy process, we transform each term in the series component-wise to new jumps satisfying pre-specified jump measure. The resulting series is the SRLMD, which is an exact Levy process, not an approximation. We give an example of alpha-stable Levy copula which has the advantage over what Tankov proposed in the follow aspects: First, it is naturally high dimensional. Second, the structure is so general that it allows from complete dependence to complete independence and can have any regular copula behavior built in. Thirdly, and most importantly, in simulation, the truncation error can be well controlled and simulation efficiency does not deteriorate in nearly independence case. For compound Poisson processes as pre-specified marginals, zero truncation error can be attained.